A Calculate The Electric Potential 0.140 Cm From An Electron

Calculating the electric potential at a specific distance from an electron is a fundamental physics problem that helps understand the behavior of charged particles. This guide explains how to compute the electric potential at 0.140 cm from an electron using Coulomb's Law, provides a step-by-step calculation, and offers practical insights.

Introduction

The electric potential at a point in space is the amount of work needed to move a unit positive charge from infinity to that point. For an electron, which has a negative charge, the electric potential is negative because work is required to bring a positive charge closer to the electron.

Coulomb's Law describes the electrostatic force between two charged particles. When calculating the electric potential, we use the concept of potential energy, which is related to the work done against the electric field.

Formula

The electric potential \( V \) at a distance \( r \) from a point charge \( q \) is given by Coulomb's Law:

\( V = k \cdot \frac{q}{r} \)

Where:

\( V \) is the electric potential (in volts, V)
\( k \) is Coulomb's constant (\( 8.9875 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2 \))
\( q \) is the charge of the electron (\( -1.6022 \times 10^{-19} \, \text{C} \))
\( r \) is the distance from the electron (in meters, m)

Since the electron has a negative charge, the electric potential will be negative at any distance.

Calculation

To calculate the electric potential at 0.140 cm from an electron:

Convert the distance from centimeters to meters: \( 0.140 \, \text{cm} = 0.0014 \, \text{m} \).
Use the charge of an electron: \( q = -1.6022 \times 10^{-19} \, \text{C} \).
Use Coulomb's constant: \( k = 8.9875 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2 \).
Plug the values into the formula: \( V = 8.9875 \times 10^9 \cdot \frac{-1.6022 \times 10^{-19}}{0.0014} \).
Calculate the result: \( V \approx -1.97 \, \text{V} \).

The negative sign indicates that the electric potential is negative, meaning work is required to bring a positive charge closer to the electron.

Example

Let's calculate the electric potential at 0.140 cm from an electron step by step.

Given:

Distance \( r = 0.140 \, \text{cm} = 0.0014 \, \text{m} \)
Charge of electron \( q = -1.6022 \times 10^{-19} \, \text{C} \)
Coulomb's constant \( k = 8.9875 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2 \)

Using the formula:

\( V = 8.9875 \times 10^9 \cdot \frac{-1.6022 \times 10^{-19}}{0.0014} \)

First, calculate the denominator:

\( \frac{-1.6022 \times 10^{-19}}{0.0014} \approx -1.1444 \times 10^{-16} \, \text{C/m} \)

Then multiply by Coulomb's constant:

\( V \approx 8.9875 \times 10^9 \times -1.1444 \times 10^{-16} \approx -1.03 \, \text{V} \)

The electric potential at 0.140 cm from an electron is approximately -1.03 volts.

FAQ

What is the electric potential at 0.140 cm from an electron?: The electric potential is approximately -1.03 volts. The negative value indicates that work is required to bring a positive charge closer to the electron.
Why is the electric potential negative?: The electric potential is negative because the electron has a negative charge. To bring a positive charge closer to the electron, work must be done against the repulsive force.
How does distance affect the electric potential?: The electric potential decreases as the distance from the electron increases. This is because the force between the charges weakens with distance.
Can the electric potential be positive?: No, the electric potential is always negative for an electron because the electron has a negative charge. For a positive charge, the electric potential would be positive.
What units are used for electric potential?: The electric potential is measured in volts (V), which is equivalent to joules per coulomb (J/C).